Properties

Label 102550r
Number of curves 2
Conductor 102550
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("102550.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 102550r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
102550.r2 102550r1 [1, 1, 1, -12975213, 17984116531] [] 2695680 \(\Gamma_0(N)\)-optimal
102550.r1 102550r2 [1, 1, 1, -15575588, 10261295781] [] 8087040  

Rank

sage: E.rank()
 

The elliptic curves in class 102550r have rank \(0\).

Modular form 102550.2.a.r

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} - 2q^{9} - q^{12} + 4q^{13} - q^{14} + q^{16} - 3q^{17} - 2q^{18} + 2q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.